Solitons and poles in the nonlinearity parameter

The KdV N-soliton solutions are analysed in terms of the perturbation parameter lambda which governs the nonlinearity. They are generated by rational Stieltjes functions Qsup((N))(lambda), each pole of which can be associated with a soliton. The asymptotic emergence of the separate solitions follows at once from the motion of the poles along the negative real lambda -axis. Successive diagonal Pade approximants of Qsup((N))(lambda) are considered. They provide a class of approximate solutions with a striking semisoliton like behaviour. (orig.)